Construction of unique mild solution and continuity of solution for the small initial data to 1-D Keller-Segel system

<p style='text-indent:20px;'>In this paper, a one-dimensional Keller-Segel system of parabolic-parabolic type which is defined on the bounded interval with Dirichlet boundary condition considered. Under assumption that initial data sufficiently small, unique mild solution to constructed and continuity for shown, by using an argument successive approximations.</p>